I'm not a fan of deep fried stuff (unpopular opinion, I know), but if I have to choose, french fries. Especially if they're not overdone, and bend when you hold then, they're softer. Mc Donald's fries, for example, are too thin and hard, not a fan.
As for the onion rings... they're alright.
I like onion rings only when they are made right (with perfectly crispy fried batter and cooked just right onion combo), which is only once in a blue moon that somebody and/or establishment will makes it right. But since I have yet to have a bad french fries experience, I voted for fries!
French fries. They need to be crispy, though. They're not very enjoyable if they're soft or crunchy. I'm picky when it comes to onion rings. They have to be crispy, and the onion inside needs to break off when I bite it. I don't like the texture of a warm onion and it coming out of the breaded part or whatever ingredients are used to surround it.